Topic  2 How do we make things speed up or slow down?

Forces

You will know that forces are pushes, pulls, or twists.  In this section we will only think about pushes and pulls.  Some key concepts in forces are essential to understand before we explain the effects of forces.

• Forces are measured in Newtons (N);

• Forces have a direction.

• Forces act in pairs.  If you push on something, it will push on you.

The blue force (from right to left) is the applied force.  The red force (from left to right) is the reaction force.

Unbalanced Forces

If the forces are in the same direction, they add up to make a resultant force.  In this picture the resultant force is shown in black:

If the forces are in opposite directions they take away.  The resultant is in the direction of the bigger of the two forces.

Note that in this case the bigger force is from right to left, so the resultant force is from right to left.

Question 1  Work out the resultant of these forces and state the direction of the resultant.

(a) 25 N from left to right and 20 N from left to right;

(b) 25 N from left to right and 20 N from right to left.  ANSWER

These forces are unbalanced; one is bigger than the other.  Wherever there are unbalanced forces on an object, the object will move (accelerate) in the direction of the bigger force.

• If the object is stationary, it will accelerate.  Therefore it will move.

• If the object is moving at a constant speed, it will accelerate to a higher speed.

Balanced Forces

When forces are balanced, they are of equal size, but opposite in direction.

Question 2.  What will be the total value of the forces above?  ANSWER

Note that this does NOT mean there is no force.  It simply means that the total of the forces add up to the value in the answer above.

When forces are balanced, it means that:

• If an object is stationary, it will continue to be stationary.  If you are sitting on a chair, your weight is balanced by an upwards force from the chair.

• If an object is moving, it will move at constant speed.  If you are pedalling a bicycle at a constant speed, the force you put into the pedals is balanced by the air resistance and friction.

This explains why a car has a maximum speed.  The engine has only a limited force it can provide.  Eventually the air resistance (and the friction) balance out the force the engine can provide, and the car cannot go any faster.

Question 3  What would happen if your weight was more than the upwards force from the chair?  ANSWER

Question 4.  Why is it harder to cycle into the wind than cycle at the same speed in still air?  ANSWER

In an aeroplane in level flight at a constant speed there are two pairs of forces acting:

• thrust from the engine (forwards force) and drag from the air resistance (backwards);

• weight acting downwards and lift from the wings acting upwards.  The lift comes from the wings moving through the air.

Question 5.  What will happen if the pilot increases the power to the engines?  ANSWER

Weight

It is important to know the difference between weight and mass.

• Mass is the amount of material in an object.  It is measured in kilograms.

• Weight is the force on a mass due to gravity.  It is measured in Newtons.

Weight is a force and is measured in Newtons.  (Repeat after me:  Weight is a Force measured in Newtons.)

It is depressing how many students still write weight in kilograms.

Think about a cosmonaut in a spaceship.  He may have a mass of 75 kg.  On the Earth that means he has a weight of 750 N.  His weight is 120 N on the Moon.  In deep space it is zero.  That doesn't mean he doesn't have material in his body.  There is simply zero gravity, so he would have zero weight.

The relationship between weight and mass is given by:

In triangle form:

On the Earth g, the gravitational field strength is 9.81 N/kg.  At GCSE it is perfectly acceptable to quote g as 10 N/kg, which is the value we will use in these notes.  The gravitational field strength is also the acceleration due to gravity, 10 m/s².

I kg = 10 N

Question 6  How much will our 75 kg cosmonaut weigh on Jupiter, where g = 32 N/kg?  ANSWER

Gravity makes objects accelerate.  All objects accelerate towards the Earth at 10 m/s², regardless of their mass.  A canon-ball and a watermelon dropped together at the same time will fall together.

Force and Acceleration

We have said that if there is an unbalanced force, then there is acceleration.  Remember that acceleration can be negative as well as positive.  This means that a force applied to a moving object can make the object slow down instead of speeding up.

Question 7  Where do rocket designers put retro rockets to make a spacecraft slow down?  Explain why.  ANSWER

Force and acceleration are linked by a simple equation which you need to learn:

Note that the force is the resultant force, so you may need to work out what it is.

In triangle form:

Worked example

Question 8  A car of mass 1200 kg accelerates at 3.0 m/s².  What is the force from the engine (ignoring friction in the transmission)?  ANSWER

Applying the Brakes

Brakes slow a car down by making extra friction, which is in the opposite direction to the movement of the car.  The acceleration is negative.

The greater the speed, the bigger the braking force that is needed to stop a car in the same distance.  If you are driving at 50 km/h, it only needs a light force on the pedal to stop the car in 100 m.  If you are driving at 100 km/h it would need a much bigger braking force to stop the car within 100 m.

When you have to stop really quickly, for example a child runs out in the road in front of you, a significant proportion of the stopping distance is taken up with the "thinking distance".  There is a reaction time while you see the emergency, realise there is an emergency, and then put your foot on the brake.  During this time, the car is still travelling at the original speed.

Have a look at http://www.highwaycode.gov.uk/index.htm

The idea of thinking distance is shown on the speed time graph below:

Question 9 What is:

(a) the thinking distance;

(b) the braking distance;

(c) the total distance;

(d) the acceleration shown for the car in the above graph?  ANSWER

The graph shows the braking performance of a car in good condition on a dry road.  The braking distance will increase if:

• the car is in poor condition, especially if the tyres are worn down;

• the road is wet or greasy.

If there is ice, there is very little friction, and braking has to be done very carefully indeed.  Ice is one of the slipperiest substances known.

Some people try to drive after have several drinks in the pub, or worse still, having taken drugs.  The kind of bedlam that results is shown in the picture below:

Why is it so dangerous to drive while drunk?   Although people have a sense of well-being, alcohol has a depressing effect on the brain.  This results in:

• loss of inhibition, making people show off by driving faster, or more aggressively;

• loss of coordination;

• less appreciation of dangerous situations;

• much slower reaction time when an emergency arises.

Now look at this graph to see how much longer it takes a drunk driver to react:

Question 10:  What is the reaction time of the drunk driver?  How much further does he travel?  ANSWER

The Law rightly takes a dim view of drinking and driving.  The least a drunk driver can expect is a heavy fine and losing their licence for at least a year.  Even when they can drive again, they can expect to pay massive insurance premiums for minimum cover for several years after.  If anyone is killed, a prison sentence will result.

Pilots of aeroplanes and train drivers also are strictly forbidden to drink while on duty, or to present themselves while under the influence of alcohol, including a hangover.

Terminal Speed

If you drop a ball bearing through thick treacly (viscous) oil, you will see that the ball bearing falls slowly at a constant speed.  It does not change speed.  This is because the weight downwards is balanced by the upwards drag force.  This constant speed is called terminal speed.  It is encountered whenever objects fall through fluids (liquids or gases).

Air is a fluid because it's a gas.  So a feather falling through air will have a terminal speed of 10 cm/s.  A sky diver falling through air has a terminal speed of about 60 m/s (about 230 km/h).    If he hit the ground at that speed, he would be killed.  To reduce the terminal speed he opens a parachute which increases the surface area (and the drag) which slows him down to about 5 m/s.

Think about a sky divers jumping from a plane:

• The drag is in the opposite direction to the weight, so the acceleration decreases.

• Then the drag (upwards force) balances the downward force (weight)

• Therefore there is no acceleration and the speed is constant.  This is terminal speed.

A speed time graph of a parachutist would look like this:

Question 11  Explain what is happening in this speed time graph.  ANSWER

Now answer Question 12.

Now try the Topic Quiz

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